Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces

We introduce the concept of a mixed g-monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. Presented theorems are generalizations of the recent fixed point theorems due to Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379–1393] and include several recent developments.     

Coupled fixed point results for mappings without mixed monotone property in partially ordered G-metric spaces

In this paper, we prove coupled fixed point results for mappings without mixed monotone property in partially ordered G-metric spaces. Also we showed that if $(X\text{,}G)$ is regular, these fixed point results holds.     

Two results in metric fixed point theory

We establish two fixed point theorems for certain mappings of contractive type. The first result is concerned with the case where such mappings take a nonempty, closed subset of a complete metric space X into X, and the second with an application of the continuation method to the case where they satisfy the Leray–Schauder boundary condition in Banach spaces.     

Coincidence and common fixed point results in partially ordered cone metric spaces and applications to integral equations

In this paper, coincidence and common fixed point results are established in a partially ordered cone metric space. An application of our results obtained to prove the existence of a common solution to integral equations is presented.     

Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces

In this paper, we establish two coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces. The theorems presented extend some results due to ?iri? (2009) [3]. An example is given to illustrate the usability of our results.     

Coupled common fixed point results in two generalized metric spaces

In this paper, study of necessary conditions for the existence of unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of our new results.     

On coincidence point and fixed point theorems for nonlinear multivalued maps

Several characterizations of MT-functions are first given in this paper. Applying the characterizations of MT-functions, we establish some existence theorems for coincidence point and fixed point in complete metric spaces. From these results, we can obtain new generalizations of Berinde-Berinde?s fixed point theorem and Mizoguchi-Takahashi?s fixed point theorem for nonlinear multivalued contractive maps. Our results generalize and improve some main results in the literature.     

Symmetric spaces approach to some fixed point results

In this paper we present a simple and unified approach to the fixed point results on cone symmetric spaces and metric type spaces based on symmetric spaces fixed point theory. We also give a new characterization of semi-metric spaces with open balls.     

A fixed point theorem for pointwise eventually nonexpansive mappings in nearly uniformly convex Banach spaces

The purpose of this paper is to prove the existence of a fixed point for a pointwise eventually nonexpansive mapping in a nearly uniformly convex Banach space. This provides an affirmative answer to a question given by Kirk and Xu [W.A. Kirk, Hong-Kun Xu, Asymptotic pointwise contraction, Nonlinear Anal. 69 (2008), 4706-4712].     

Note on “Coupled fixed point theorems for contractions in fuzzy metric spaces”

In the paper “Coupled fixed point theorems for contractions in fuzzy metric spaces” by Sedghi et al. [S. Sedghi, I. Altun, N. Shobec, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis 72 (2010) 1298-1304], a coupled common fixed point result was presented. However, our purpose is to show that this result and its proof are false. We give a counterexample and also explain how to correct this result. As a modification, we state and prove a coupled fixed point theorem under some hypotheses of fuzzy metric and t-norm.     

Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces

Generalizations of the Edelstein-Suzuki theorem [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal. TMA 71 (2009), 5313-5317], including versions of the Kannan, Chatterjea and Hardy-Rogers-type fixed point results for compact metric spaces, are proved. Also, abstract metric versions of these results are obtained. Examples are presented to distinguish our results from the existing ones.     

Some new results and generalizations in metric fixed point theory

The main purpose of this paper is the study of the generalization of some results given in [M. Berinde, V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2007) 772-782] and references therein. Some generalizations of the Mizoguchi-Takahashi fixed point theorem, Kannan’s fixed point theorems and Chatterjea’s fixed point theorems are established by using our new fixed point theorems.     

A fixed point theorem for weakly Zamfirescu mappings

In [5], Zamfirescu (1972) gave a fixed point theorem that generalizes the classical fixed point theorems by Banach, Kannan, and Chatterjea. In this paper, we follow the ideas of Dugundji and Granas to extend Zamfirescu’s fixed point theorem to the class of weakly Zamfirescu maps. A continuation method for this class of maps is also given.     

Common fixed point results for mappings of Perov type

Fixed point results for mappings f and g are obtained where f and g are related in the sense of Das and Naik, ?iri?, Hardy and Rogers, and all are of Perov type. We consider both normal and non‐normal cones. The theory is illustrated with some examples.     

Some recent results in metric fixed point theory

This is a survey of recent results on best approximation and fixed point theory in certain geodesic spaces. Some of these results are related to fundamental fixed point theorems in topology that have been known for many years. However the metric approach is emphasized here. Dedicated to Edward Fadell and Albrecht Dold on the occasion of their 80th birthdays     

Fixed point results for multimaps in CAT(0) spaces

Common fixed point results for families of single-valued nonexpansive or quasi-nonexpansive mappings and multivalued upper semicontinuous, almost lower semicontinuous or nonexpansive mappings are proved either in CAT(0) spaces or R-trees. It is also shown that the fixed point set of quasi-nonexpansive self-mapping of a nonempty closed convex subset of a CAT(0) space is always nonempty closed and convex.     

Krasnoselskii‐type fixed point theorems with applications to Hammerstein integral equations in spaces

In this paper, we study fixed point theorems and new variants of some nonlinear altenatives of Krasnoselskii type in Banach spaces by using measures of weak noncompactness. Then we give an application to solve a nonlinear Hammerstein integral equation in L¹ spaces.     

Fixed point theorems for generalized metrically inward maps

We prove fixed point results for multimaps satisfying a generalized metric (or an α-metric) inwardness condition. Our results extend, generalize or improve several known results.     

Two abstract approaches in vectorial fixed point theory

In this paper a fixed point theory is established for operators defined on Cartesian product spaces. Two abstract approaches are presented in terms of closure operators and of general functionals called measures of deviations from zero resembling the measures of noncompactness. In particular, we give vectorial versions to Mönch’s fixed point theorems. An application is included to illustrate the theory.     

Coupled fixed points in partially ordered metric spaces and application

In this paper, we prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.